# Course Descriptions

To help students plan for their future, we overview the study of Mathematics, and how it is applied to the 21st century science and industry. Mathematics curriculum is explained along with student oriented programs.

Series, convergence test, Taylor’s theorem, partial differentiation, double and triple integration, Green’s theorem, Stokes’ theorem.

Series, convergence test, Taylor’s theorem, partial differentiation, double and triple integration, Green’s theorem, Stokes’ theorem.

Series, convergence test, Taylor’s theorem, partial differentiation, double and triple integration, Green’s theorem, Stokes’ theorem.

Students experience basic research on Mathematics. They are guided to initiate and develop research, and summarize research results through seminar presentation.

Higher order ordinary differential equations, Laplace transformations, convolution, systems of ordinary differential equations.

Overview of the mathematics research over the undergraduate level, introduction to international trend and achievements.

Recommended Prerequistes : MATH 110

Basic concepts and properties of an infinite set and the properties of a compact set in a metric space: Countable Set, Uncountable Set, Well Ordered Set, Axiom of Choice, Cardinal Number, Ordinal Number, Metric Space, Compact Set.

Simultaneous linear equations, matrix and Gaussian elimination, inverse matrix, Gram-Shmidt orthogonalization, orthogonal projections, least squares, eigenvalues, eigenvectors, diagonalization and sign of matrix.

Analytic functions, Cauchy-Riemann equations, integration in complex domain, Taylor and Laurent series, residues and poles, Cauchy‘s theorem, conformal mapping.

Elements of probability, expectation, probability distribution, estimation, hypothesis test, correlation, analysis of variance, This course is designed for scientists as well as engineers.

Equivalent of Math 230. For non-mathematics majors

Sets, relations, algorithm and its analysis, regression relation, graph theory, Boolean algebra, logical networks, language and grammar, design and construction of finite state machines, Turing machine.

Group theory, Ring theory, ideal, maximal ideal, polynomial rings, the fundamental theorem of abelian groups, field theory, Galois theory.

Congruence and residues, reduced residue systems, primitive roots, quadratic residues, continues fractions.

Number systems, set theory, metric spaces, numerical sequences and series, Riemann-Stieltjes integral, uniform convergence, equicontinuity, power series, inverse function and implicit function theorem, Lebesgue measure.

Recommended Prerequistes : MATH 311

Parabolic, hyperbolic and elliptic equations. Dirichlet and Neumann boundary value problem, existence and uniqueness theorems, Maximum principle, existence and uniqueness, potential theory, separation of variables, Fourier series method, Hilbert space methods

Sets and logics, Topological space, continuous functions, metric spaces, connection, compactness, separation axiom and countability axiom, Tychonoff’s theorem.

Euclid geometry, Helbert’s axioms, hyperbolic geometry, non-Euclidean geometry, independence of the parallel postulate, geometric transformations.

Applied probability and introductory statistics, Data processing by package programs, regression analysis, standard parameter statistics methods

Introductory Partial differential equations from engineering sciences and physics, vector caculus, separation of variables, Fourier series and integrals, numerical methods, tensor method related to fluid mechanics and electro-magnetic fields, complex variable methods for engineering problem

Recommended Prerequistes : MATH 203

Numerical methods for simultaneous linear equations, numerical methods for nonlinear equations, interpolation and polynomial approxiation, numerical differentiation and integration, initial value problems for ordinary differential equations, stability.

Refer to CSED 232

Recommended Prerequistes : MATH 301

Rings and modules, commutative groups of a finitely generated direct decomposition of a finitely generated module over a PID, linear transformations and matrices, Jordan canonical forms, characteristic polynomials.

Recommended Prerequistes : MATH 302

Affine space and algebraic sets. Hilbert’s Nullstellensatz, affine and projective algebraic varieties, algebraic varieties, Riemann-Roch theorem.

Recommended Prerequistes : MATH 203, 301

Group representations, characters of group, character’s properties, character table, Induced representation, Mackey’s Theorem, Transitive groups, Induced characters of symmetric groups, Some applications like Burnside’s Theorem dimension

Recommended Prerequistes : MATH 210

Schwarz Lemma, Conformal mapping, Rouch’s Theorem, Hurwitz’s Theorem, topological property of H(G),

Harmonic function related to Poisson Integral formula

Recommended Prerequistes : MATH 311

Power series solutions, Bessel functions, Poincar-Bendixson’s theorem, Liapunov’s method,

Recommended Prerequistes : MATH 311

We survey the basic properties of the Fourier series, including a brief history and different kinds of convergence, and various applications. Furthermore, after discussing the basic properties and applications of the Fourier transform in the real number space R, we will study Fourier transform in the Euclidean space R^n.

Recommended Prerequistes : MATH 321

Triangulation, Classification of surfaces, maps and graphs, Fundamental Groups

Differential forms, Frenet formula, covariant vector, connection forms, structural equations, second fundamental form, curvature, geodesics, parallel vector fields, Gauss-Bonnet theorem.

Recommended Prerequistes : MATH 230

Order statistics, maximum likelihood estimator, Pitman estimates, consistence statistics, parameter confidence interval, Cramer-Rao limit, Fisher’s information matrix, limit of estimator deviation

Recommended Prerequistes : MATH 230

random variables, distribution functions, moment generating functions, random variables’ properties, limit theorems,

Recommended Prerequistes : MATH 230

Topics : Actuarial models, Principles in stochastic modelling, Premium rates & losses, Life table analysis, Regression models, Time series analysis, Simulation

Recommended Prerequistes : MATH 230

Deformation of the natural phenomena to mathematical model problem, stage of the solution seeking by mathematical way of thinking, Population dynamics model, Epidemic dispersion model

Elasticity, fluid mechanics, Cauchy stress tensor, pressure momentum, force, turbulence, hyperelasticity, Eulerian and Lagrangian coordinates, vorticity.

Change of variables , contravariant/covariant tensor, metric tensor, Ricci tensor, Application to geometry, geodesic, fundamental forms, Applications to analytic mechanics, Newtonian Principle, Applications to continuum mechanics

Introductory concepts, linear codes, Hamming codes and Golay codes, finite fields, cyclic codes, BCH codes, weight distributions, The MacWilliams equation, designs, Assumus-Mattson theorem, uniqueness of codes

Classical cryptosystems, basic number theory, data encryption standard (DES), RSA algorithm, discrete logarithms and ElGamal cryptosystem, digital signatures, secret sharing schemes, introductory Elliptic Curve Cryptosystems

Recommended Prerequistes : MATH 351

Numerical solutions for polynomials, Newton’s method, orthogonal polynomials and least-squares approximation, eigenvalues and eigenvectors, boundary value problems for ordinary differential equations,

Generating Functions, Recurrence Relations, Polya enunerations, Covering circuits, Colorings

Prerequisite : MATH 261

Graph and tree, cycles, Euler tours, Hamilton cycles, Ramsey, Turan, Schur, Kuratowski theorem, Networks.

Graphs and tree, cycles, Euler tours, Hamilton cycles, Ramsey, Turan, Schur, Kuratowski’s theorem, Networks.

Recommended Prerequisite : IMEN 203

Fixed income securities(cash flow, structure of interest rates), contemporary portfolio theory(Mean-Variance, CAPM, APT), Theories of Derivatives(Forward, Future, Swap, option,) MATLAB practice, various mathematical approach to te financial models distinct from traditional finance

Boolean Algebra, first order postulate, recursive function, Zermelo-Frankel set theory, ordinals and order, choice axiom, incompleteness theorem

An adequate subject is chosen with supervisor’s guidance. Students are expected to give presentation and lead discussions to deepen the knowledge they have attained from regular courses. This course can be taken multiple times.

Lecturer and students choose an adequate subject. This course can be taken multiple times.